We present HST narrow-band near-infrared imaging of Pa \alpha and Pa \beta emission of 48 local Luminous Infrared Galaxies ( LIRGs ) from the Great Observatories All-Sky LIRG Survey ( GOALS ) . These data allow us to measure the properties of 810 spatially resolved star-forming regions ( 59 nuclei and 751 extra-nuclear clumps ) , and directly compare their properties to those found in both local and high-redshift star-forming galaxies . We find that in LIRGs , the star-forming clumps have radii ranging from \sim 90 - 900 pc and star formation rates ( SFRs ) of \sim 1 \times 10 ^ { -3 } to 10 M _ { \odot } yr ^ { -1 } , with median values for extra-nuclear clumps of 170 pc and 0.03 M _ { \odot } yr ^ { -1 } . The detected star-forming clumps are young , with a median stellar age of 8.7 Myrs , and a median stellar mass of 5 \times 10 ^ { 5 } M _ { \odot } . The SFRs span the range of those found in normal local star-forming galaxies to those found in high-redshift star-forming galaxies at z = 1 - 3 . The luminosity function of the LIRG clumps has a flatter slope than found in lower-luminosity , star-forming galaxies , indicating a relative excess of luminous star-forming clumps . In order to predict the possible range of star-forming histories and gas fractions , we compare the star-forming clumps to those measured in the MassiveFIRE high-resolution cosmological simulation . The star-forming clumps in MassiveFIRE cover the same range of SFRs and sizes found in the local LIRGs and have total gas fractions that extend from 10 to 90 % . If local LIRGs are similar to these simulated galaxies , we expect future observations with ALMA will find a large range of gas fractions , and corresponding star formation efficiencies , among the star-forming clumps in LIRGs .